"The United States must greatly strengthen and expand its nuclear capability until such time as the world comes to its senses regarding nukes," Trump wrote.
Putin then responded to Trump's comments before more than 1,000 journalists in Moscow. He told the gathering of regional and international correspondents that there was nothing unusual about Trump's riposte.
"We will never look to be dragged into an arms race and to spend resources that we can't afford," Putin said.
With Trump poised to succeed Barack Obama as president in January, his foray into social media to talk about weapons sparked concern that sensitive parts of US policy may be exposed to pointless speculation.
Laicie Heeley is a nuclear expert at the Stimson Center, a nonpartisan anti-nuclear proliferation think tank in Washington.
She told AFP that it was reckless "for Trump to tweet on the topic without offering details.
"To make such a loaded statement without context or follow-up is irresponsible at best," she said. "We could be talking about a return to the Cold War here, when the threat of a nuclear catastrophe was very real. Russian rhetoric is already moving in that direction. It wouldn't take a lot to bring us back there."
During the eight years of Obama's administration, policy was steered towards reducing the nuclear arsenal. In 2010, Obama and the then Russian president, Dmitry Medvedev, signed a treaty aimed at cutting the amount of weapons.
"The problems between Russia and the United States over the past year due to Syria and Ukraine have slowly created this problem," said Beyza Unal, a nuclear weapons policy researcher at the London based thinktank Chatham House.
"That's why you are seeing a provocative discourse and the rhetoric from both sides. It's not helpful towards the understanding of the main problem."
The US, Russia and other countries such as France and Britain are faced with choices over upgrading antiquated nuclear defence systems. However, gleaming nuclear hardware in the silos have been unable to reduce the number of atrocities.
Terrorist attacks have scarred France and Britain - countries which boast deterrents.
French defence chiefs want the miltary budget to rise from 1.7 to 2 per cent of gross domestic product by 2022. The soil is fertile for such an increase, according to Jean-Marie Collin, vice-president of the Initiative for Nuclear Disarmament.
"The generals say they want the money for the army," said Collin. "For most people 'the army' means tanks, fighter planes and troops, but in reality this money is going for the nuclear deterrent."
With the US and Russia holding more than 14,000 nuclear missiles between them, and their military industrial complexes unlikely to be starved of cash over the next few years, the weapons debate will focus on servicing an increasingly paranoid public either with belligerent rhetoric or with more police and troops on the streets.
"Nuclear weapons symbolise power," said Unal. "Although it really is a power you cannot use. I've looked at the fetishistic discourse on nuclear weapons and the power that comes with it. I think the nuclear weapons states are into that fetish. It's no longer about the quantity of nuclear weapons, it's about the quality of nuclear weapons."